FRACTRAN
Posted: February 6th, 2017, 2:29 pm
What always interested me about cellular automata was creating large computational structures using simple rules. In that spirit is FRACTRAN, a simple game with fractions invented(?popularized?) by John Conway.
A FRACTRAN program consists of a list of fractions f1, f2, f3... fN and an input value Z. For the first fraction f in the list for which f*Z is an integer, replace Z with f*Z. Halt when there is no such fraction.
Amazingly, this process is capable of universal computation. It functions like a register machine where the exponents in the prime factorization of Z are the values in various registers. The 'division' allows a test-dec command. For example, the program
when given a value of (2^a)(3^b) returns a value of (2^a+b).
More complicated programs follow: This one starts with Z=2 and eventually gives Z=2^3, 2^5, 2^7, 2^11... generating the prime numbers.
This is a program I created myself - when given 2^a it returns 2^(a/2) if a is even and 2^(3a+1) if a is odd and repeats, calculating a Collatz sequence.
A FRACTRAN program consists of a list of fractions f1, f2, f3... fN and an input value Z. For the first fraction f in the list for which f*Z is an integer, replace Z with f*Z. Halt when there is no such fraction.
Amazingly, this process is capable of universal computation. It functions like a register machine where the exponents in the prime factorization of Z are the values in various registers. The 'division' allows a test-dec command. For example, the program
Code: Select all
2/3More complicated programs follow: This one starts with Z=2 and eventually gives Z=2^3, 2^5, 2^7, 2^11... generating the prime numbers.
Code: Select all
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55/1Code: Select all
832/33
16/11
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